Higher-page Hodge theory of compact complex manifolds

Popovici, Dan ; Stelzig, Jonas ; Ugarte, Luis (Universidad de Zaragoza)

Resumen: On a compact @ @-manifold X, one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as HkdR(X) = p+q=kHp;q(X), where the Hp;q(X) are
canonically isomorphic to the Dolbeault cohomology groups Hp;q @ (X). For an arbitrary nonnegative integer r, we introduce the class of page-r-@ @-manifolds by requiring the analogue of the Hodge decomposition to hold on a compact complex manifold X when the usual Dolbeault cohomology groups Hp; q @ (X) are replaced by the spaces Ep; q r+1(X) featuring on the (r + 1)-st page of the Frolicher spectral sequence of X. The class of page-r-@ @-manifolds coincides with the usual class of @ @-manifolds when r = 0 but may increase as r
increases. We give two kinds of applications. On the one hand, we give a purely numerical characterisation of the page-r-@ @-property in terms of dimensions of various cohomology vector spaces. On the other hand,we obtain several classes of examples, including all complex parallelisable nilmanifolds and certain families of solvmanifolds and abelian nilmanifolds. Further, there are general results about the behaviour of this new class under standard constructions like blow-ups and deformations.

Idioma: Inglés

DOI: 10.2422/2036-2145.202111_014

Año: 2024

Publicado en: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE 25, 3 (2024), 1431–1464
ISSN: 0391-173X

Factor impacto JCR: 1.3 (2024)

Categ. JCR: MATHEMATICS rank: 71 / 483 = 0.147 (2024) - Q1 - T1

Factor impacto CITESCORE: 2.3 - Mathematics (miscellaneous) (Q2) - Theoretical Computer Science (Q3)

Factor impacto SCIMAGO: 1.775 - Theoretical Computer Science (Q1) - Mathematics (miscellaneous) (Q1)

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)